Felix has a utility function U$=$W$12$

U

$=$

W

$1$

$2$

$,$ where W

W

is his wealth in millions of dollars and U

U

is the utility he obtains from that wealth. In the final stage of a game show, the host offers Felix a choice between $($A$)$ $$4$ million for sure, or $($B$)$ a gamble that pays $$1$ million with probability $0\mathrm{.}4$ and $$9$ million with probability $0\mathrm{.}6.$

Use the blue curve $($circle points$)$ to graph Felix's utility function at wealth levels of $$0,$ $$1$ million, $$4$ million, $$9$ million, and $$16$ million.

Utility Function

$0$

$2$

$4$

$6$

$8$

$10$

$12$

$14$

$16$

$18$

$20$

$5\mathrm{.}0$

$4\mathrm{.}5$

$4\mathrm{.}0$

$3\mathrm{.}5$

$3\mathrm{.}0$

$2\mathrm{.}5$

$2\mathrm{.}0$

$1\mathrm{.}5$

$1\mathrm{.}0$

$0\mathrm{.}5$

$0$

Utility $($Thousands$)$

Wealth $($Millions of dollars$)$

True or False: Felix is risk averse.

True

False

Choice offers Felix a higher expected prize. $($Hint: The expected value of a random variable is the weighted average of the possible outcomes, where the probabilities are the weights.$)$

Choice offers Felix a higher expected utility.

Felix should pick choice $.$